Poliedros duais e algumas aplicações

Abstract

In this paper, we study the duality of polyhedra, highlighting the teaching of geo metry and the historical context of its emergence. We present four very interesting classes of polyhedra: regular polyhedra, Kepler-Poinsot polyhedra, Archimedes solid, and Catalan solid, describing a brief bibliography on the contributions of these great mathematicians, including Plato. We highlighted all de nitions and results relevant to the study, emphasizing the importance of addressing this topic in the classroom. In addition, we introduced some transformations involving polyhedra and made the planning of the studied polyhedra in order to facilitate the reader's understanding and understanding. In the chapter devoted to applications, we suggest some problems that can be addressed in spatial geometry classes, especially by the elementary school teacher. Finally, we teach the step by step of building an Archimedean solid using Geogebra.